Particulate matter is defined as a mixture of airborne solid particles and liquid droplets that can be inhaled and may cause serious health problems. Such elements are currently measured utilizing air quality monitoring devices that provide information on PM 10 and PM 2.5 levels giving information on pollution levels. However, many difficulties are encountered in the determination of nanosized ...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

in this paper the concept of an $omega$- almost boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $omega$- almost boolean ring over a locally boolean space.

‎let $i$ be an ideal in a regular local ring $(r,n)$‎, ‎we will find‎ ‎bounds on the first and the last betti numbers of‎ ‎$(a,m)=(r/i,n/i)$‎. ‎if $a$ is an artinian ring of the embedding‎ ‎codimension $h$‎, ‎$i$ has the initial degree $t$ and $mu(m^t)=1$‎, ‎we call $a$ a {it $t-$extended stretched local ring}‎. ‎this class of‎ ‎local rings is a natural generalization of the class of stretched ...

the freiheitssatz of magnus for one-relator groups is one of the cornerstones of combinatorial group theory. in this short note which is mostly expository we discuss the relationship between the freiheitssatz and corre-sponding results in free power series rings over fields. these are related to results of schneerson not readily available in english. this relationship uses a faithful representa...

Background: The appropriate colon cleansing is a major determinant of quality of colonoscopy. The aim of this study was to compare the efficacy and tolerability of the morning (AM) PEG (polyethylene glycol) solution to previous-evening (PM) PEG solution for the afternoon colonoscopy. Methods: This comparative study compared the AM to PM prep for afternoon outpatient colonoscopy. The subjects r...